Max-Min SINR Analysis of STAR-RIS Assisted Massive MIMO Systems with Hardware Impairments

Reconfigurable intelligent surface (RIS) has
emerged as a cost-effective solution to improve wireless
communication performance through just passive reflection.
Recently, the concept of simultaneously transmitting and
reflecting RIS (STAR-RIS) has appeared but the study of
minimum signal-to-interference-plus-noise ratio (SINR) and
the impact of hardware impairments (HWIs) remain open.
In addition to previous works on STAR-RIS, we consider a
massive multiple-input multiple-output (mMIMO) base station
(BS) serving multiple user equipments (UEs) at both sides of
the RIS. Specifically, in this work, focusing on the downlink
of a single cell, we derive the minimum SINR obtained by the
optimal linear precoder (OLP) with HWIs in closed form. The
OLP maximises the minimum SINR subject to a given power
constraint for any given passive beamforming matrix (PBM).
Next, we obtain deterministic equivalents (DEs) for the OLP
and the minimum SINR, which are then used to optimise the
PBM. Notably, based on the DEs and statistical channel state
information (CSI), we optimise simultaneously the amplitude
and phase shift by using a projected gradient ascent algorithm
(PGAM) for both energy splitting (ES) and mode switching
(MS) STAR-RIS operation protocols with reduced feedback,
which is quite crucial for STAR-RIS systems that include the
double number or variables compared to reflecting only RIS.
Simulations verify the analytical results, shed light on the
impact of HWIs, and demonstrate the better performance of
STAR-RIS compared to conventional RIS. Also, a benchmark
full instantaneous CSI (I-CSI) based design is provided and
shown to result in higher SINR but lower net achievable
sum-rate than the statistical CSI based design because of large
overhead associated with the acquisition of full I-CSI acquisition.
Thus, not only do we evaluate the impact of HWIs but we also
propose a statistical CSI based design that provides higher net
sum-rate with low overhead and complexity.